Decision Variables

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

Question

Dokument Courier Services has two Vans which it uses for deliveries. The first (X) can carry 10 of Product A or 4 of Product B. The second (Y) can carry 3 of A or 5 of Product B. Minimum deliveries are 200 of A and 150 of B. In order to maintain roadworthiness, each lorry must be used for a minimum of two journeys per week. Suppose the running costs are GHS20000.00 per journey for Lorry X and GHS 15000.0 per journey for Lorry Y. find the number of deliveries made by each lorry to minimize costs. If the aim of the manager of Dokument is to minimize costs. (a) Identify the decision variables. (b) Formulate the problem into a linear programming problem (LPM). (c) Display the LPM on a graph and shade the critical region.

(d) Use the graphical approach to solving the LPM

Answer

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Tags: critical region, Decision Variables, formulation, graph, graphical method, Linear Programming, Minimization
Level: Level 2

Topic: Linear Programming, Mathematical relationships in business problems
Series: APR 2024

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

Question

Joycarpap Ltd manufactures and sells three models of affordable toys: Car, Joy, and Pap. Each model requires a specific amount of fabrication hours, material worth, and assembly hours as shown in the table below:

There are 210 fabrication hours available, 170 hours of assembly available, and materials worth GH¢200 in stock. Market research conducted by the company revealed that demand for the toys is such that, in whatever combination of the three models produced, all of the output can be sold within a week.

Each Car contributes GH¢15 to profit, each Joy contributes GH¢20 to profit, and each Pap contributes GH¢14 to profit. Using $X_{1}$ , $X_{2}$ , $X_{3}$ as decision variables, and $S_{1}$ , $S_{2}$ , $S_{3}$ as slack variables, and $P$ as total profit:

Required:
i) Formulate a linear programming problem. (4 marks)

ii) Set up the initial Simplex Tableau. (4 marks)

iii) Determine the total profit in the first iteration. (5 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Constraints, Decision Variables, Linear Programming, Profit Maximization, Simplex Method
Level: Level 1

Topic: Linear Programming
Series: MAY 2019

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

Question

(d) Use the graphical approach to solving the LPM

Answer

Find Related Questions by Tags, levels, etc.

Tags: critical region, Decision Variables, formulation, graph, graphical method, Linear Programming, Minimization
Level: Level 2

Topic: Linear Programming, Mathematical relationships in business problems
Series: APR 2024

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

Question

Required:
i) Formulate a linear programming problem. (4 marks)

ii) Set up the initial Simplex Tableau. (4 marks)

iii) Determine the total profit in the first iteration. (5 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Constraints, Decision Variables, Linear Programming, Profit Maximization, Simplex Method
Level: Level 1

Topic: Linear Programming
Series: MAY 2019

Question Tag: Decision Variables

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QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

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QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

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QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

You're reporting an error for "QT – May 2019 – L1 – Q7a – Linear Programming"

QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization

Formulate and solve a linear programming problem using graphical method to minimize running costs for two lorries delivering minimum quantities of two products with capacity and usage constraints.

You're reporting an error for "QMFD – APR 2024 – L2 – Q1 – Linear Programming in Delivery Optimization"

QT – May 2019 – L1 – Q7a – Linear Programming

Formulate a linear programming model for maximizing profit using decision variables and constraints.

You're reporting an error for "QT – May 2019 – L1 – Q7a – Linear Programming"

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